The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1 2X  1  1  1  0  1 2X^2+X  1  1  1  1  1  1 2X  1  0  1  1  1  1 2X^2+X  1  1 2X  1  1  1 X^2+2X  1 X^2+X 2X^2+X  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1 X^2+X  0  1 2X  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X+2 2X  1 2X^2+1 2X^2+2X+1  2  1 2X^2+1  1 2X^2+X+2 2X+2  0 X+1 2X 2X^2+X  1  2  1  0 2X+2 X+1 2X^2+2X+1  1 2X 2X^2+X+2  1 2X^2+X X^2+X+1  0  1 2X+2  1  1  2 X^2+2X 2X^2+2X+1 X+1 X^2+2X+1 2X^2+1 X^2+2X+1 2X^2+X+1  1 X^2+2X+1 2X^2+1 X^2+2 2X^2+X+2 2X X+1  1  1 X^2  1 2X+1
 0  0 2X^2  0  0  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2  0 X^2 2X^2  0  0  0 2X^2 2X^2 X^2  0 X^2  0 2X^2 2X^2 2X^2  0 2X^2  0 X^2  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2  0  0 X^2  0 2X^2 X^2 X^2 2X^2  0  0 2X^2 2X^2  0  0 2X^2 X^2 X^2
 0  0  0 X^2  0 X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 X^2  0  0 2X^2 2X^2 2X^2 X^2  0  0  0 X^2 X^2 2X^2 2X^2  0 2X^2 2X^2 X^2 2X^2  0  0 X^2  0 X^2 2X^2 X^2  0 X^2 2X^2  0 X^2 2X^2 X^2 2X^2  0 X^2 X^2  0 2X^2 2X^2 2X^2  0  0  0 X^2 X^2 2X^2 2X^2
 0  0  0  0 2X^2 2X^2 X^2  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 X^2  0  0 2X^2 2X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 2X^2 2X^2 2X^2  0  0 2X^2  0 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2  0  0  0 2X^2 X^2  0 2X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+508x^114+432x^115+54x^116+1390x^117+1206x^118+324x^119+2756x^120+2196x^121+648x^122+3694x^123+2430x^124+432x^125+2062x^126+1008x^127+330x^129+18x^130+122x^132+42x^135+8x^138+10x^141+6x^144+4x^150+2x^156

The gray image is a linear code over GF(3) with n=549, k=9 and d=342.
This code was found by Heurico 1.16 in 20.6 seconds.